A series acceleration for the Clausen function is given by Cl 2 ( θ ) θ = 1 − log | θ | + ∑ n = 1 ∞ ζ ( 2 n ) n ( 2 n + 1 ) ( θ 2 π ) 2 n {\displaystyle {\frac {\operatorname {Cl} _{2}(\theta )}{\theta }}=1-\log |\theta |+\sum _{n=1}^{\infty }{\frac {\zeta (2n)}{n(2n+1)}}\left({\frac {\theta }{2\pi }}\right)^{2n}} which holds for | θ | < 2 π {\displaystyle |\theta |<2\pi } . Une des accélérations de série de la fonction de Clausen est donnée par : Cl 2 ( θ ) θ = 1 − ln | θ | + ∑ n = 1 ∞ ζ ( 2 n ) n ( 2 n + 1 ) ( θ 2 π ) 2 n
